Double auction mechanisms on Markovian networks

• A double auction mechanism has been studied for a class of exchange economies.
• Buyers and sellers each form a time non-homogeneous Markovian chain.
• Convergence results with and without noises are established.
• A numerical example is given to demonstrate the formation of bubbles and crashes.

This paper studies the double auction (DA) mechanism in Ma and Li (2011) for a class of exchange economies. We extend their results to more general cases where sellers and buyers each form a complex time non-homogeneous Markovian chain, as specified in Ram et al. (2009), in the communication of their private information. A numerical example is also provided. Both bubbles and crashes are observed in the example, consistent with results of our theorems. Our example and theoretical results provide new evidence that a DA mechanism, widely utilized in real exchange markets, may contribute to the excess volatility identified in Shiller (1981) and LeRoy and Porter (1981).